Karl used 2 inch by 2 inch square tile to cover a 14 inch by 12 inch piece of cardboard. Each tile weighs 3 ounces. What is the combined weight of the tiles Karl used to cover the piece of cardboard?

The value of c=12 will makes the equation true. for the given expression.

Here in the question we have expression:

[tex]\dfrac{3\sqrt{x^3}}{cy^4}}=\dfrac{x}{4y^3\sqrt{y}}[/tex]

By solving the above equation we will get:

[tex]12\sqrt{x}=c\sqrt{y}[/tex]

So value of c=12 will makes the equation true. for the given expression.

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The correct value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

To find the value of [tex]\( c \)[/tex], we start by simplifying the given equation:

[tex]\[ 3\sqrt{\frac{x^3}{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

First, we simplify the left side of the equation by applying the cube root to both the numerator and the denominator:

[tex]\[ \frac{3\sqrt{x^3}}{3\sqrt{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] , and the cube root of [tex]\( y^4 \)[/tex] is [tex]\( y \)[/tex] times the cube root of [tex]\( y \)[/tex], which is [tex]\( y \cdot y^{1/3} \)[/tex]. Simplifying further, we get:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

Now, we simplify the right side of the equation:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x \cdot 3\sqrt{y}}{4y} \][/tex]

Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are positive, we can multiply both sides by [tex]\( 4y \)[/tex] to eliminate the denominators:

[tex]\[ \frac{4yx}{3\sqrt{c} \cdot y} = x \cdot 3\sqrt{y} \][/tex]

Simplifying, we get:

[tex]\[ \frac{4x}{3\sqrt{c}} = 3x\sqrt{y} \][/tex]

Now, we can divide both sides by [tex]\( x \)[/tex] since [tex]\( x > 0 \)[/tex]:

[tex]\[ \frac{4}{3\sqrt{c}} = 3\sqrt{y} \][/tex]

Next, we square both sides to eliminate the square root:

[tex]\[ \left(\frac{4}{3\sqrt{c}}\right)^2 = (3\sqrt{y})^2 \][/tex]

[tex]\[ \frac{16}{9c} = 9y \][/tex]

Since [tex]\( y > 0 \)[/tex], we can multiply both sides by [tex]\( 9c \)[/tex] to get rid of the denominator:

[tex]\[ 16 = 81cy \][/tex]

Now, we divide both sides by [tex]\( y \)[/tex]:

[tex]\[ \frac{16}{y} = 81c \][/tex]

Finally, we multiply both sides by [tex]\( y \)[/tex] to solve for [tex]\( c \)[/tex]:

[tex]\[ 16 = 81c \][/tex]

[tex]\[ c = \frac{16}{81} \][/tex]

[tex]\[ c = \left(\frac{2^4}{3^4}\right) \][/tex]

[tex]\[ c = \left(\frac{2}{3}\right)^4 \][/tex]

[tex]\[ c = \left(\frac{3}{2}\right)^{-4} \][/tex]

[tex]\[ c = 64 \][/tex]

Therefore, the value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

ANSWER

A.

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

EXPLANATION

Given

[tex]f(x) = \frac{x + 3}{4} [/tex]

Let

[tex]y= \frac{x + 3}{4} [/tex]

Interchange x and y

[tex]x= \frac{y + 3}{4} [/tex]

Solve for y,

[tex]4x = y + 3[/tex]

y=4x-3

This implies that,

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

Answer:

A. Step One

B. She multiplied straight across in the proportion instead of diagonally

Step-by-step explanation:

Answer:

A. Step One

B. She multiplied straight across in the proportion instead of diagonally

Answer:

Global extrema:  none.  Local extrema:  (0, 0) and (4, -32)

Step-by-step explanation:

ƒ(x) = x3 – 6x2 should be written as  ƒ(x) = x^3 – 6x^2.  Use " ^ " to denote exponentiation, please.

One way to answer this problem would be to make a careful graph of ƒ(x) = x^3 – 6x^2.  Notice that this graph begins in Quadrant III and ends in Quadrant I; this is one outcome of its being an ODD function.  The graph will increase, reach a peak (a local max), decrease, reach a valley (a local min) and then grow from then on.

Another way is to use calculus.  You don't say what course you're in, so I can't be sure that calculus would make sense to you.

Find the first derivative of  ƒ(x) = x^3 – 6x^2.  It is f '(x) = 3x^2 - 12x.  Set this derivative = to 0 and find the roots.  Hint:  find the roots of 3x^2(x - 4).  They are x = 0 and x = 4.  At x = , y = f(0) = 0.  Thus, the local max is

(0, 0).  At x = +4, y = f(4) = 64 - 6(16) = -32.  Thus, the local min is at (4, -32 ).

This graph rises without bound as x goes to ∞, and decreases without bound as x goes to -∞.  Thus, there is neither a global max nor a global min.  

Answer: D

Step-by-step explanation:

Subtract the like terms:

6x^2 - 2x^2 = 4x^2

3x - -4x = 3x+4x = 7x

1 - 5 = -4

Now combine them to get the final answer:

4x^2 + 7x - 4

Answer: [tex]6x^2+11[/tex]

Step-by-step explanation:

Given the polynomial of degree 3:

[tex]24x^3 - 54x^2 + 44x -99[/tex]

You can observe make two groups or two terms each:

[tex](24x^3 + 44x) - (54x^2 + 99)[/tex]

The Greatest Common Factor (GCF), is the highest number that divides into two or more numbers without leaving remainder.

 You can observe that the GCF of both set are factored out ([tex]4x[/tex] and [tex]9[/tex]), then, you can find  the common factor that is missing from both sets of parentheses with this procedure:

[tex](\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)[/tex]

You can observe that the common factor that is missing from both sets of parentheses is:

[tex]6x^2+11[/tex]

Answer:

q = 20

Step-by-step explanation:

1/5q = 4

q = 20

where are the signs between the 5 and 48j, and k and 2? is at multiplication? cause you use parentheses only for that.

If it is multiplication... then 3j * 3k = 9jk

48j * 5 = 240j * k =240jk * 2 = 480jk / 9jk = 53.3333333333jk

Answer: $72.30

Step-by-step explanation:

[tex]I=P*r*t[/tex]

P is the principal amount, $482.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 3 years

The answer you're looking for is $72.30. To find this answer multiply $482 by 0.05 (five percent). From there you'll get 24.1, then multiply that by 3 (three years), and you'll get $72.30/ Hope that helps! :)

Answer:

Second degree trinomial.

Step-by-step explanation:

Answer:

AA

Step-by-step explanation:

we know that

The AA postulate states that two triangles are similar if they have two corresponding angles that are congruent

In the triangle JKL find the measure of angle L

Remember that in a triangle the sum of the interior angles must be equal to 180 degrees

so

∠J+∠K+∠L=180°

substitute the given values

105°+50°+∠L=180°

∠L=180°-155°=25°

Compare the measure of two corresponding angles of triangles JKL and MPN

∠J=∠M=105°

∠L=∠N=25°

therefore

The triangles JKL and MPN are similar by AA similarity postulate

An Isosceles triangle means it has two sides that measures the same.

When we have two sides that measures the same also means that they have the same angles.

If one angel measures 140 that means that the other angles are 20 and 20

Because the angles of the triangle has to sum to 180

In an isosceles triangle, two angles are same and the sum of all angles is 180 degrees. If one angle is 140 degrees, the other two angles must sum to 40 degrees, and since they are equal, each would measure 20 degrees.

In an isosceles triangle, two of the angles are equal, and the third angle, also known as the base angle, is different. The total sum of the angles in any triangle, including an isosceles triangle, is always 180 degrees. Thus, if one of the angles measures 140 degrees, the remaining two angles must sum up to 40 degrees. Since these two angles are equal (as it is an isosceles triangle), each of them would measure 20 degrees. Thus, in the given isosceles triangle, the other two angles would measure 20 degrees each.

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Answer:

the opposite sides are of equal length; - the diagonals bisect each other; - the opposite angles are congruent; - the sum of any two consecutive angles is equal to 180 . Rhombis (plural of rhombus) have additional properties. Theorem 1. In a rhombus, the diagonals are the angle bisectors.

Step-by-step explanation:

The diagonals of a rhombus bisect opposite interior angles because they create congruent triangles that have equal corresponding angles.

The question addresses a geometry concept about the properties of a rhombus. To justify that the diagonals of a rhombus bisect opposite interior angles, we can consider the definition of a rhombus as a special type of parallelogram where all four sides are of equal length. Additionally, we know that in a parallelogram, opposite sides are parallel. By drawing the diagonals of a rhombus, we create congruent triangles because of the properties of parallelograms and the fact that all sides of a rhombus are equal. Each diagonal will bisect the angle from which it is drawn because in these congruent triangles, the corresponding angles are equal. This means that the diagonals bisect each other and they bisect the opposite interior angles into equal parts.

Hello there!

The answer is the first option.

Remember that congruent = same size and same shape, and this is the only option that has both of those things. In the second and forth options, the sizes are different making those options not correct. In the 3rd option, the shape is slightly different since one triangle is not as stretched out as the other.

I hope this was helpful and have a great day!

Since the two sides and one angle in figure 1 are the same as a result they are congruent.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

While the similarity law for triangles is defined as the law to prove that two triangles have the same shape, it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Thus, the two sides and one angle in figure 1 are the same as a result they are congruent.

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Answer:

c = 25

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to find c

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

c² = 7² + 24² = 49 + 576 = 625

Take the square root of both sides

c = [tex]\sqrt{625}[/tex] = 25

Answer:

C=25

Step-by-step explanation:

Square both 24 and 7,Then add them together.

576+49=C

625=C

Square root 625

C=25

Just by itself? No it is not.

Answer:

Coordinates of A': will NOT be the same

Coordinates of C': will NOT be the same

Perimeter of ABC: will be the same

Area of A'B'C': will be the same

Measure of ∠B: will be the same

Slope of A'C': will be the same

Step-by-step explanation:

We have a triangle ABC that will be translated (moved) 2 units down, 3 units to the right.

Since the triangle is moved, then the coordinates of every summit (A, B and C) will be affected.  So,

Coordinates of A': will NOT be the same

Coordinates of C': will NOT be the same

However, since the triangle is only moved, not transformed in any way, not scaled up/down for example the following will remain the same:

Perimeter of ABC: will be the same

Area of A'B'C': will be the same

Measure of ∠B: will be the same

Since the triangle is only translated, not rotated or reflected the following will remain the same:

Slope of A'C': will be the same

[tex]\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x^2+15x+\boxed{?}^2\implies \stackrel{\textit{we know the middle term is}}{2\sqrt{x^2}\cdot \sqrt{\boxed{?}^2}\implies 2x\boxed{?}}\qquad then\qquad 2x\boxed{?}=15x \\\\\\ \boxed{?}=\cfrac{15x}{2x}\implies \boxed{?}=\cfrac{15}{2}\qquad \impliedby \textit{we should add that much \underline{squared}} \\\\[-0.35em] ~\dotfill\\\\ x^2+15x+\left( \cfrac{15}{2} \right)^2\implies \left(x+ \cfrac{15}{2} \right)^2[/tex]

Answer:

£210

Step-by-step explanation:

A decrease of 30% represents 70% of the original cost.

100% represents the original cost

Divide the price by 70 to find 1% then multiply by 100 for original cost

original cost = [tex]\frac{147}{70}[/tex] × 100 = 2.1 × 100 = £210

Answer:

210

Step-by-step explanation:

let original price =x

x×70÷100=147

x=147×100÷70=210

Answer:

x = z - w

Step-by-step explanation:

Given

w + x = z ( isolate x by subtracting w from both sides )

x = z - w

Answer:

x = z - w

Step-by-step explanation:

Take w to the other side and subtract with z to make x the subject

A leap year consists of 366 days.

52 weeks + 2 days.

These 2 days can be: (mon,tue),(tue,wed),(wed,thu),(thu,fri),(fri,sat)(sat,sun)(sun,mon)

Thus, the total number of cases = 7.

The number of cases in which we get Friday = 2(Thu, Fri)(Fri, Sat).

Therefore the required probability = 2/7.

Answer:

3x^2+6x+4 is the answer :D

The sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given polynomials:

= (6x + 7 + x²) + (2x² - 3)

To add the polynomials, we must add the like terms:

= 3x² + 6x +4

Thus, the sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.

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ANSWER

A. (8)(-4.5)

EXPLANATION

The given expression is

[tex] - 4.5 \times - 8[/tex]

We evaluate this to obtain:

[tex]- 4.5 \times - 8 = 36[/tex]

For option A

[tex](8) \times - 4.5 = - 36[/tex]

For option B

[tex]8 \times 4.5 = 36[/tex]

For option C,

[tex] - 8 \times - 4.5 = 36[/tex]

For option D

[tex](4.5)(8) = 36[/tex]

The odd one is option A.

The correct answer is A.

A because it would become negative while the rest become positive.

Answer:

15.5 or 15 1/2

arrange all numbers least to greatest and cross out each number until u get to the last two, once u get to the last two add them and divide them by two:

Answer:

Question 10: [tex]f(x)=1/2x-1[/tex] Question 13: [tex]f(-2)=-1[/tex] Question 11: [tex]f(8)=60[/tex]

Step-by-step explanation:

For Question 10:

The functionis in the form of [tex]f(x)[/tex]. We know the slope is [tex]\frac{1}{2}[/tex] (rise 1 run 2)and the y intercept is -1 (where the line goes through the y axis). We can then put the function is slope intercept form ([tex]y=mx+b[/tex]) and we would have [tex]f(x)=1/2x-1[/tex].

For Question 13:

To evaluate the function[tex]f(x)=\frac{3}{2} x-4[/tex] for [tex]f(-2)[/tex] we need to plug -2 into the function as x. [tex]f(-2)=\frac{3}{-2} (-2)-4[/tex]. [tex]\frac{3}{-2}[/tex] times -2 would equal 3 because the negatives cancle out. 3-4 equals -1 so the solution is [tex]f(-2)=-1[/tex].

For question 11:

Same as question 13. plug 8 into x in [tex]f(x)=x^2-4[/tex]. This would be [tex]f(8)=(8)^2-4[/tex]. 8 squared is 64 and 64-4 is 60. Therefore [tex]f(8)=60[/tex].

M<2=105. They must add up to 180.

The measure of the angle is 6°

A complementary angle consists of two angles who's sum is 90 degrees. Since there are two we know this for sure:

1st angle: x (unknown value)

2nd angle: x-78 (78 less then its complement)

total: 90

If we put the equation together we get:  x+x-78= 90

x+x-78+78=90+78

2x=168

2x/2=168/2

x=84

Now we know that x = 84, know we gonna find the 2nd angle:

1st: x=84

2nd: 84-78 = 6

total: 84+6=90

Since m<4 and m<8 both add up to 180 degrees. Combine 2x + 20 and 3x - 5 and set it equal to 180. By subtracting 15 to the other side and dividing five to the other side you get x=33. Plug 33 back into the angle measurement separate equations to find degree angle measurement. Your welcome.

Final answer:

The solutions of the given system can be found by solving the equations simultaneously using the method of substitution. The solution is (x, y) = (-30, 55).

Explanation:

The solutions of the given system of equations can be found by solving it simultaneously. We have the following equations:

X+y = 25

| 2x+y= -5

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:

Therefore, the solution to the system is (x, y) = (-30, 55).